The hosts closed day two on 158 for four in response to their opponents' first-innings 391, 233 runs behind with Chigumbura unbeaten on 45 at stumps.
Malcolm Waller was with him on 30 as the pair put on an unbroken stand of 61.
It helped dig Zimbabwe out of a hole after Bangladesh quick Robiul Islam had removed both openers to help reduce them to 47 for three at tea.
Having hit a quickfire 24, Robiul had both Vusi Sibanda (10) and Regis Chakabva (12) caught behind by Mushfiqur Rahim off outside edges as Zimbabwe slipped from 23 without loss to 26 for two.
Shakib Al Hasan then bowled Hamilton Masakadza for 14 shortly before the break. The hosts mounted a fightback in the final session of the day, with Brendan Taylor making 36 before falling to Sohag Gazi.
Chigumbura came to the crease and upped the rate, his 45 coming from 49 balls and including five fours.
Earlier, Bangladesh resumed on 300 for six and continued to build a promising total, helped by 77 from Nasir Hossain.
Ziaur Rahman was the first man to fall in the morning, lbw to Keegan Meth playing across the line. Gazi provided useful support for Hossain by adding 21 before he was caught at long on by Chigumbura off Graeme Cremer.
Nasir's 103-ball knock, which featured 11 fours, was finally ended by Cremer, who bowled him between bat and pad. Robiul hit an unbeaten 24 off 18 balls, including two maximums, to take Bangladesh towards 400 before his partner Sajidul Islam went for a duck.